Kenan Scribe - Box Plots

A box plot by definition is a graphical way of depicting numerical values through their five number summaries. So what does this mean? Let's say for example that I were to hand you 9 balls, each with a random number written on the sides. A box plot would be an easy way to show a bit about the numbers you have received in a neat graphical form.

Five number summaries: Every box plot consists of five unique points, the minimum, the first quartile, the median (or second quartile), the third quartile, and the maximum. After arranging the numbers you receive from smallest to largest you can then begin to decide which numbers are what.

The minimum is simply the smallest number in the data set.

The median is the number directly in the middle of the series. If there are an odd number of numbers then you will not be able to select one single number in the middle. You will take the middle two, add them together and divide the sum by 2, thus finding this average (or the median). This will be the median of your data set.

The maximum is the largest number in your data set, the opposite of the minimum.

The two quartiles are slightly more tricky, but still very simple to find. For the first quartile, look to all the numbers to the left of the median. Find the median of this new data set and you will have your first quartile for all of your numbers. This works inversely with the third quartile. Look to the right of the median, find the median of these numbers and you will have your third quartile. But why do you go from the first directly to third quartile you ask You want to know where the second quartile is? Well, if the data set is to be broken into quarters, there will be four parts of it. A quarter is a fourth. The second quartile will be the number directly in the middle, so we have already found it. The second quartile is the median!

REMEMBER! Box plots must always be drawn along a number line!

Let's look at a box plot, shall we?

These are three very simple horizontal box plots. As you can see, there appears to be lines coming from the box shape we had all assumed would be the graph. These are known as whiskers. At the far left end lies the minimum of the data, at the far right, the maximum. The box starts on the left on the first quartile. The box ends on the third quartile and the whisker that leads to the maximum begins. The median is the line down the middle of the box plot.

Here is a data set of 7 random numbers I just thought of. I have put them in order for you already.

2, 4, 5, 9, 13, 16, 17.

What is the minimum?

What is Q1? (first quartile)

What is the median?

What is Q3? (third quartile)

What is the maximum?

Minimum: 2

Q1: 4

Median: 9

Q3: 16

Maximum: 17

If you were to make this into a box plot, what would it look like?

Sadly, I can't draw a box plot in computer speak so I'm going to tell you what it would look like. The box plot would be set on a number line from 0 to 20, just because that would look nice and encompass all the numbers in our data set. The left whisker would begin at 2 and then continue until the side of the box began at 4. The box would end at 16. There will be a line through the box at 9 to denote the median. The right whisker will begin from the side of the box and go until 17. This is a fairly jacked up box plot but that's what happens when I make up a bunch of random numbers. Box plots are an easy and informative way to collect vital data on an otherwise overwhelming set of numbers.